We prove that the Shortest Vector Problem (SVP) on point lattices
is NP-hard to approximate for any constant factor under
polynomial time randomized reductions with one-sided error that
produce no false positives. We also prove inapproximability for
quasi-polynomial factors under the same kind of reductions
running in subexponential time. Previous hardness results for
SVP either incurred two-sided error, or only proved hardness for
small constant approximation factors. Close similarities between
our reduction and recent results on the complexity of the
analogous problem on linear codes make our new proof an
attractive target for derandomization, paving the road to a
possible NP-hardness proof for SVP under deterministic polynomial
time reductions.